# Electronics and Communication Engg - GATE 2007 Paper Solution

If E denotes expectation, the variance of a random variable X is given by

The following plot shows a function y which varies linearly with x. The value of the integral $I=\int\limits_1^2y\;dx$ is

For |x|<< 1, coth(x) can be approximated as

$\underset{\theta \to 0}{\mathrm{lim}}\frac{\mathrm{sin}\left(\theta /2\right)}{\theta }$ is

Which one of the following functions is strictly bounded?

For the function ${e}^{-x}$, the linear approximation around x = 2 is:

An independent voltage source in series with an impedance ZS = RS + jXS delivers a maximum average power to a load impedance ZL when

The RC circuit shown in the figure is

The electron and hole concentrations in an intrinsic semiconductor are ni per cm3 at 300 K. Now, if acceptor impurities are introduced with a concentration of NA per cm3 (where NA >> ni), the electron concentration per cm3 at 300 K will be

In a p+n junction diode under reverse bias, the magnitude of electric field is maximum at

The correct full wave rectifier circuit is:

 (A) (B) (C) (D)

In a transconductance amplifier, it is desirable to have

X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two‘s complement format. The sum of X and Y represented in two‘s complement format using 6 bits is:

The Boolean function Y = AB + CD is to be realized using only 2-input NAND gates. The minimum number of gates required is:

If the closed-loop transfer function of a control system is given as $T\left(s\right)=\frac{s-5}{\left(s+2\right)\left(s+3\right)}$, then it is

If the Laplace transform of a signal y(t) is $Y\left(s\right)=\frac{1}{s\left(s-1\right)}$, then its final value is

If $R\left(\tau \right)$ is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true?

If S(f) is the power spectral density of a real, wide-sense stationary random process, then which of the following is ALWAYS true?

A plane wave of wavelength $\lambda$ is traveling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The $\stackrel{\to }{E}$ field of the plane wave can be represented as (E0 is constant)
If C is a closed curve enclosing a surface S, then the magnetic field intensity $\stackrel{\to }{H}$, the current density $\stackrel{\to }{J}$ and the electric flux density $\stackrel{\to }{D}$ are related by